arXiv subjects

Muhammad Omer Bin Saeed

Publications and source records attributed to Muhammad Omer Bin Saeed.

6 recordsLinked to original sources

arXiv2025

Solving Newell-Whitehead-Segel and Allen-Cahn Equations Employing Physics-Informed Neural Networks: A Comparative Analysis with Spline Methods

This study focuses on the solution of partial differential equations (PDEs) by using physics-informed neural networks (PINNs). The Newell-Whitehead-Segel (NWS) equation and the Allen-Cahn equation belong to fundamental PDEs used mostly in various scientific disciplines. Different methods, including analytical and numerical approaches, have been proposed for solving these equations alongside the recently introduced PINN method. This study provides a detailed and comprehensive comparison between the developed PINN method and the state-of-the-art spline numerical solution for the NWS and Allen-Cahn equation. Furthermore, the computational time of the trained PINN models is evaluated to determine their computational efficiency. The findings show that PINN is significantly better than spline methods in solving both problems.

math.AP↗

arXiv2025

Enhancing PINN Performance Through Lie Symmetry Group

This paper presents intersection of Physics informed neural networks (PINNs) and Lie symmetry group to enhance the accuracy and efficiency of solving partial differential equation (PDEs). Various methods have been developed to solve these equations. A Lie group is an efficient method that can lead to exact solutions for the PDEs that possessing Lie Symmetry. Leveraging the concept of infinitesimal generators from Lie symmetry group in a novel manner within PINN leads to significant improvements in solution of PDEs. In this study three distinct cases are discussed, each showing progressive improvements achieved through Lie symmetry modifications and adaptive techniques. State-of-the-art numerical methods are adopted for comparing the progressive PINN models. Numerical experiments demonstrate the key role of Lie symmetry in enhancing PINNs performance, emphasizing the importance of integrating abstract mathematical concepts into deep learning for addressing complex scientific problems adequately.

math.AP↗

arXiv2019

A Complete Transient Analysis for the Incremental LMS Algorithm

The incremental least mean square (ILMS) algorithm was presented in \cite{Lopes2007}. The article included theoretical analysis of the algorithm along with simulation results under different scenarios. However, the transient analysis was left incomplete. This work presents the complete transient analysis, including the learning behavior. The analysis results are verified through several experimental results.

cs.DS↗

arXiv2015

A Unified Analysis Approach for LMS-based Variable Step-Size Algorithms

The least-mean-squares (LMS) algorithm is the most popular algorithm in adaptive filtering. Several variable step-size strategies have been suggested to improve the performance of the LMS algorithm. These strategies enhance the performance of the algorithm but a major drawback is the complexity in the theoretical analysis of the resultant algorithms. Researchers use several assumptions to find closed-form analytical solutions. This work presents a unified approach for the analysis of variable step-size LMS algorithms. The approach is then applied to several variable step-size strategies and theoretical and simulation results are compared.

cs.DS↗

arXiv2014

Low-Complexity Particle Swarm Optimization for Time-Critical Applications

Particle swam optimization (PSO) is a popular stochastic optimization method that has found wide applications in diverse fields. However, PSO suffers from high computational complexity and slow convergence speed. High computational complexity hinders its use in applications that have limited power resources while slow convergence speed makes it unsuitable for time critical applications. In this paper, we propose two techniques to overcome these limitations. The first technique reduces the computational complexity of PSO while the second technique speeds up its convergence. These techniques can be applied, either separately or in conjunction, to any existing PSO variant. The proposed techniques are robust to the number of dimensions of the optimization problem. Simulation results are presented for the proposed techniques applied to the standard PSO as well as to several PSO variants. The results show that the use of both these techniques in conjunction results in a reduction in the number of computations required as well as faster convergence speed while maintaining an acceptable error performance for time-critical applications.

cs.NE↗

arXiv2013

An accelerated CLPSO algorithm

The particle swarm approach provides a low complexity solution to the optimization problem among various existing heuristic algorithms. Recent advances in the algorithm resulted in improved performance at the cost of increased computational complexity, which is undesirable. Literature shows that the particle swarm optimization algorithm based on comprehensive learning provides the best complexity-performance trade-off. We show how to reduce the complexity of this algorithm further, with a slight but acceptable performance loss. This enhancement allows the application of the algorithm in time critical applications, such as, real-time tracking, equalization etc.

cs.NE↗